Some more Fano threefolds with a multiplicative Chow-K\"unneth decomposition

TL;DR

This paper identifies new families of Fano threefolds and double covers of projective spaces that possess a multiplicative Chow-K"unneth decomposition, leading to injectivity results for certain Chow subrings.

Contribution

It provides explicit examples of Fano threefolds and double covers with multiplicative Chow-K"unneth decompositions, expanding the class of varieties known to have this property.

Findings

Fano threefolds with multiplicative Chow-K"unneth decomposition identified

Double covers of projective spaces admit such decompositions

Tautological subrings inject into cohomology for these varieties

Abstract

We exhibit several families of Fano threefolds with a multiplicative Chow-K\"unneth decomposition, in the sense of Shen-Vial. As a consequence, a certain tautological subring of the Chow ring of powers of these threefolds injects into cohomology. As a by-product of the argument, we observe that double covers of projective spaces admit a multiplicative Chow-K\"unneth decomposition.